| name | two-phase-flow |
| description | Two-phase gas-liquid flow — flow regimes, void fraction, Lockhart-Martinelli pressure drop, Baker chart, two-phase multiplier, steam-water quality, drift-flux model. |
| metadata | {"priority":7,"promptSignals":{"phrases":["two-phase flow","two phase","void fraction","Lockhart-Martinelli","flow regime","quality","steam water"],"minScore":3}} |
Two-Phase Gas-Liquid Flow — Complete Skill
Flow Regimes (Horizontal Pipe)
Depends on gas and liquid superficial velocities (j_G = Q_G/A, j_L = Q_L/A):
Stratified: low velocity, gravity separates phases (horizontal only)
Wavy: stratified with waves at interface
Slug: intermittent gas plugs + liquid slugs; most common in pipelines
Plug (Elongated bubble): elongated gas bubbles in liquid
Annular: gas core, liquid film on wall; high gas velocity
Dispersed bubble (froth): gas bubbles in liquid continuum; high liquid velocity
Mist: liquid droplets in gas; very high gas velocity
Baker Chart (horizontal): map of G_L [lb/hr ft²] vs. G_G [lb/hr ft²] with regime boundaries
Quality and Void Fraction
Definitions
Quality: x = ṁ_G / (ṁ_G + ṁ_L) = mass fraction vapor (x=0 saturated liquid, x=1 saturated vapor)
Void fraction: α = A_G/A = fraction of flow area occupied by gas
Slip ratio: S = u_G/u_L = actual velocity ratio gas/liquid (S ≥ 1)
Relation (with slip):
α = x / (x + S(1-x)(ρ_G/ρ_L))
Homogeneous (S=1): α = x/(x + (1-x)ρ_G/ρ_L) = xv_G / (xv_G + (1-x)v_L)
Two-Phase Pressure Drop — Lockhart-Martinelli
Martinelli Parameter
X = (ΔP/ΔL)_L^0.5 / (ΔP/ΔL)_G^0.5
(ΔP/ΔL)_L = pressure gradient if only liquid flowed (Darcy-Weisbach with G_total as liquid)
(ΔP/ΔL)_G = pressure gradient if only gas flowed
For turbulent-turbulent (both phases turbulent):
X_tt = ((1-x)/x)^0.9 × (ρ_G/ρ_L)^0.5 × (μ_L/μ_G)^0.1
Two-phase multiplier:
Φ_L² = 1 + C/X + 1/X² [Chisholm correlation]
C = 20 (turb-turb), 12 (visc-turb), 10 (turb-visc), 5 (visc-visc)
(ΔP/ΔL)_TP = Φ_L² × (ΔP/ΔL)_L
Chisholm Correlation (Simpler)
Φ_LO² = 1 + (Γ² - 1)[B x^(2-n)/2 (1-x)^(2-n)/2 + x^(2-n)]
Γ² = (ΔP/ΔL)_GO / (ΔP/ΔL)_LO (both phases as all-liquid or all-gas)
Drift Flux Model (Void Fraction)
α = j_G / (C₀ j + V_Gj)
j = j_G + j_L (total superficial velocity)
C₀ = profile factor (≈ 1.2 for bubbly/slug; 1.0 for annular)
V_Gj = drift velocity [m/s] (gas relative to mixture):
Bubbly: V_Gj = 1.53[σg(ρ_L-ρ_G)/ρ_L²]^0.25
Slug: V_Gj = 0.35√(gD)
Annular: V_Gj ≈ 0
Pressure Drop Components
ΔP_total = ΔP_friction + ΔP_acceleration + ΔP_gravity
ΔP_gravity = ρ_mix g L sin θ (θ = inclination angle)
ρ_mix = α ρ_G + (1-α) ρ_L
Acceleration (evaporation or condensation):
ΔP_acc = G²[(1-x_2)²/(ρ_L(1-α₂)) + x_2²/(ρ_G α₂) - same at inlet 1]
G = total mass flux [kg/m²s]
Critical Flow (Choked Two-Phase)
Maximum mass flux at critical (sonic) conditions:
G_crit = √[-(dP/d(1/ρ_mix))] at throat
Homogeneous: G_crit = [P_0 ρ_mix,0 / (x_0 v_fg/v_g + 1/(γ P_0))]^0.5 (approximate)
Output
Provide: flow regime identification, void fraction α [—], quality x [—], two-phase pressure gradient (ΔP/ΔL)_TP [Pa/m], Martinelli parameter X_tt, two-phase multiplier Φ_L², total ΔP [kPa] over pipe length.
